Properties

Label 567.2.w.a.46.6
Level $567$
Weight $2$
Character 567.46
Analytic conductor $4.528$
Analytic rank $0$
Dimension $132$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(37,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.w (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 46.6
Character \(\chi\) \(=\) 567.46
Dual form 567.2.w.a.37.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.306313 + 1.73719i) q^{2} +(-1.04461 - 0.380207i) q^{4} +(0.723302 + 4.10205i) q^{5} +(-1.55501 + 2.14055i) q^{7} +(-0.783518 + 1.35709i) q^{8} +O(q^{10})\) \(q+(-0.306313 + 1.73719i) q^{2} +(-1.04461 - 0.380207i) q^{4} +(0.723302 + 4.10205i) q^{5} +(-1.55501 + 2.14055i) q^{7} +(-0.783518 + 1.35709i) q^{8} -7.34759 q^{10} +(0.428940 - 2.43264i) q^{11} +(0.108160 - 0.0907572i) q^{13} +(-3.24222 - 3.35702i) q^{14} +(-3.82067 - 3.20592i) q^{16} -0.702677 q^{17} +6.46502 q^{19} +(0.804060 - 4.56005i) q^{20} +(4.09457 + 1.49030i) q^{22} +(4.27608 - 3.58805i) q^{23} +(-11.6052 + 4.22394i) q^{25} +(0.124532 + 0.215695i) q^{26} +(2.43823 - 1.64481i) q^{28} +(-0.100910 - 0.0846735i) q^{29} +(4.35670 + 1.58571i) q^{31} +(4.33878 - 3.64067i) q^{32} +(0.215239 - 1.22068i) q^{34} +(-9.90538 - 4.83046i) q^{35} +(-0.387945 + 0.671941i) q^{37} +(-1.98032 + 11.2310i) q^{38} +(-6.13358 - 2.23244i) q^{40} +(2.52108 - 2.11544i) q^{41} +(-5.66175 + 2.06071i) q^{43} +(-1.37298 + 2.37808i) q^{44} +(4.92331 + 8.52742i) q^{46} +(-5.59334 + 2.03581i) q^{47} +(-2.16389 - 6.65714i) q^{49} +(-3.78296 - 21.4542i) q^{50} +(-0.147492 + 0.0536827i) q^{52} +(-1.85992 + 3.22148i) q^{53} +10.2891 q^{55} +(-1.68654 - 3.78745i) q^{56} +(0.178004 - 0.149363i) q^{58} +(2.78047 - 2.33309i) q^{59} +(0.205027 - 0.0746237i) q^{61} +(-4.08919 + 7.08269i) q^{62} +(0.00796973 + 0.0138040i) q^{64} +(0.450523 + 0.378034i) q^{65} +(2.66458 + 15.1116i) q^{67} +(0.734024 + 0.267163i) q^{68} +(11.4256 - 15.7279i) q^{70} +(7.04066 + 12.1948i) q^{71} +(-6.36370 - 11.0222i) q^{73} +(-1.04845 - 0.879758i) q^{74} +(-6.75343 - 2.45805i) q^{76} +(4.54018 + 4.70095i) q^{77} +(1.00160 - 5.68035i) q^{79} +(10.3874 - 17.9914i) q^{80} +(2.90267 + 5.02758i) q^{82} +(1.84338 + 1.54678i) q^{83} +(-0.508248 - 2.88242i) q^{85} +(-1.84557 - 10.4667i) q^{86} +(2.96524 + 2.48813i) q^{88} -0.904179 q^{89} +(0.0260800 + 0.372651i) q^{91} +(-5.83104 + 2.12233i) q^{92} +(-1.82327 - 10.3403i) q^{94} +(4.67616 + 26.5198i) q^{95} +(-1.73081 + 0.629965i) q^{97} +(12.2275 - 1.71991i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.306313 + 1.73719i −0.216596 + 1.22838i 0.661519 + 0.749928i \(0.269912\pi\)
−0.878115 + 0.478449i \(0.841199\pi\)
\(3\) 0 0
\(4\) −1.04461 0.380207i −0.522305 0.190104i
\(5\) 0.723302 + 4.10205i 0.323471 + 1.83449i 0.520212 + 0.854037i \(0.325853\pi\)
−0.196741 + 0.980455i \(0.563036\pi\)
\(6\) 0 0
\(7\) −1.55501 + 2.14055i −0.587738 + 0.809051i
\(8\) −0.783518 + 1.35709i −0.277015 + 0.479805i
\(9\) 0 0
\(10\) −7.34759 −2.32351
\(11\) 0.428940 2.43264i 0.129330 0.733469i −0.849311 0.527893i \(-0.822982\pi\)
0.978641 0.205576i \(-0.0659068\pi\)
\(12\) 0 0
\(13\) 0.108160 0.0907572i 0.0299983 0.0251715i −0.627665 0.778483i \(-0.715989\pi\)
0.657664 + 0.753312i \(0.271545\pi\)
\(14\) −3.24222 3.35702i −0.866518 0.897202i
\(15\) 0 0
\(16\) −3.82067 3.20592i −0.955168 0.801481i
\(17\) −0.702677 −0.170424 −0.0852121 0.996363i \(-0.527157\pi\)
−0.0852121 + 0.996363i \(0.527157\pi\)
\(18\) 0 0
\(19\) 6.46502 1.48318 0.741588 0.670855i \(-0.234073\pi\)
0.741588 + 0.670855i \(0.234073\pi\)
\(20\) 0.804060 4.56005i 0.179793 1.01966i
\(21\) 0 0
\(22\) 4.09457 + 1.49030i 0.872965 + 0.317733i
\(23\) 4.27608 3.58805i 0.891624 0.748161i −0.0769115 0.997038i \(-0.524506\pi\)
0.968535 + 0.248877i \(0.0800614\pi\)
\(24\) 0 0
\(25\) −11.6052 + 4.22394i −2.32104 + 0.844789i
\(26\) 0.124532 + 0.215695i 0.0244226 + 0.0423012i
\(27\) 0 0
\(28\) 2.43823 1.64481i 0.460783 0.310841i
\(29\) −0.100910 0.0846735i −0.0187385 0.0157235i 0.633370 0.773849i \(-0.281671\pi\)
−0.652109 + 0.758125i \(0.726115\pi\)
\(30\) 0 0
\(31\) 4.35670 + 1.58571i 0.782487 + 0.284802i 0.702209 0.711971i \(-0.252197\pi\)
0.0802776 + 0.996773i \(0.474419\pi\)
\(32\) 4.33878 3.64067i 0.766995 0.643586i
\(33\) 0 0
\(34\) 0.215239 1.22068i 0.0369132 0.209345i
\(35\) −9.90538 4.83046i −1.67431 0.816498i
\(36\) 0 0
\(37\) −0.387945 + 0.671941i −0.0637778 + 0.110466i −0.896151 0.443749i \(-0.853648\pi\)
0.832373 + 0.554215i \(0.186982\pi\)
\(38\) −1.98032 + 11.2310i −0.321250 + 1.82190i
\(39\) 0 0
\(40\) −6.13358 2.23244i −0.969804 0.352980i
\(41\) 2.52108 2.11544i 0.393727 0.330376i −0.424336 0.905505i \(-0.639493\pi\)
0.818063 + 0.575129i \(0.195048\pi\)
\(42\) 0 0
\(43\) −5.66175 + 2.06071i −0.863409 + 0.314255i −0.735495 0.677530i \(-0.763050\pi\)
−0.127914 + 0.991785i \(0.540828\pi\)
\(44\) −1.37298 + 2.37808i −0.206985 + 0.358509i
\(45\) 0 0
\(46\) 4.92331 + 8.52742i 0.725902 + 1.25730i
\(47\) −5.59334 + 2.03581i −0.815873 + 0.296953i −0.716048 0.698052i \(-0.754051\pi\)
−0.0998253 + 0.995005i \(0.531828\pi\)
\(48\) 0 0
\(49\) −2.16389 6.65714i −0.309127 0.951021i
\(50\) −3.78296 21.4542i −0.534992 3.03409i
\(51\) 0 0
\(52\) −0.147492 + 0.0536827i −0.0204535 + 0.00744445i
\(53\) −1.85992 + 3.22148i −0.255480 + 0.442504i −0.965026 0.262155i \(-0.915567\pi\)
0.709546 + 0.704659i \(0.248900\pi\)
\(54\) 0 0
\(55\) 10.2891 1.38738
\(56\) −1.68654 3.78745i −0.225374 0.506119i
\(57\) 0 0
\(58\) 0.178004 0.149363i 0.0233731 0.0196123i
\(59\) 2.78047 2.33309i 0.361986 0.303742i −0.443596 0.896227i \(-0.646297\pi\)
0.805582 + 0.592485i \(0.201853\pi\)
\(60\) 0 0
\(61\) 0.205027 0.0746237i 0.0262510 0.00955458i −0.328861 0.944378i \(-0.606665\pi\)
0.355112 + 0.934824i \(0.384443\pi\)
\(62\) −4.08919 + 7.08269i −0.519328 + 0.899502i
\(63\) 0 0
\(64\) 0.00796973 + 0.0138040i 0.000996216 + 0.00172550i
\(65\) 0.450523 + 0.378034i 0.0558805 + 0.0468893i
\(66\) 0 0
\(67\) 2.66458 + 15.1116i 0.325530 + 1.84617i 0.505925 + 0.862578i \(0.331151\pi\)
−0.180395 + 0.983594i \(0.557738\pi\)
\(68\) 0.734024 + 0.267163i 0.0890135 + 0.0323983i
\(69\) 0 0
\(70\) 11.4256 15.7279i 1.36562 1.87984i
\(71\) 7.04066 + 12.1948i 0.835573 + 1.44725i 0.893563 + 0.448937i \(0.148197\pi\)
−0.0579909 + 0.998317i \(0.518469\pi\)
\(72\) 0 0
\(73\) −6.36370 11.0222i −0.744815 1.29006i −0.950281 0.311393i \(-0.899205\pi\)
0.205467 0.978664i \(-0.434129\pi\)
\(74\) −1.04845 0.879758i −0.121880 0.102270i
\(75\) 0 0
\(76\) −6.75343 2.45805i −0.774671 0.281957i
\(77\) 4.54018 + 4.70095i 0.517402 + 0.535723i
\(78\) 0 0
\(79\) 1.00160 5.68035i 0.112689 0.639090i −0.875180 0.483798i \(-0.839257\pi\)
0.987869 0.155292i \(-0.0496319\pi\)
\(80\) 10.3874 17.9914i 1.16134 2.01150i
\(81\) 0 0
\(82\) 2.90267 + 5.02758i 0.320547 + 0.555203i
\(83\) 1.84338 + 1.54678i 0.202337 + 0.169781i 0.738326 0.674444i \(-0.235617\pi\)
−0.535989 + 0.844225i \(0.680061\pi\)
\(84\) 0 0
\(85\) −0.508248 2.88242i −0.0551272 0.312642i
\(86\) −1.84557 10.4667i −0.199013 1.12866i
\(87\) 0 0
\(88\) 2.96524 + 2.48813i 0.316095 + 0.265236i
\(89\) −0.904179 −0.0958428 −0.0479214 0.998851i \(-0.515260\pi\)
−0.0479214 + 0.998851i \(0.515260\pi\)
\(90\) 0 0
\(91\) 0.0260800 + 0.372651i 0.00273392 + 0.0390644i
\(92\) −5.83104 + 2.12233i −0.607928 + 0.221268i
\(93\) 0 0
\(94\) −1.82327 10.3403i −0.188056 1.06652i
\(95\) 4.67616 + 26.5198i 0.479764 + 2.72088i
\(96\) 0 0
\(97\) −1.73081 + 0.629965i −0.175737 + 0.0639632i −0.428390 0.903594i \(-0.640919\pi\)
0.252653 + 0.967557i \(0.418697\pi\)
\(98\) 12.2275 1.71991i 1.23517 0.173738i
\(99\) 0 0
\(100\) 13.7289 1.37289
\(101\) 6.23114 + 5.22855i 0.620021 + 0.520260i 0.897810 0.440382i \(-0.145157\pi\)
−0.277789 + 0.960642i \(0.589602\pi\)
\(102\) 0 0
\(103\) −1.11235 6.30845i −0.109603 0.621590i −0.989281 0.146021i \(-0.953353\pi\)
0.879678 0.475569i \(-0.157758\pi\)
\(104\) 0.0384205 + 0.217893i 0.00376744 + 0.0213662i
\(105\) 0 0
\(106\) −5.02660 4.21781i −0.488226 0.409670i
\(107\) 5.96628 + 10.3339i 0.576782 + 0.999016i 0.995846 + 0.0910589i \(0.0290251\pi\)
−0.419063 + 0.907957i \(0.637642\pi\)
\(108\) 0 0
\(109\) −0.160232 + 0.277531i −0.0153475 + 0.0265826i −0.873597 0.486650i \(-0.838219\pi\)
0.858250 + 0.513232i \(0.171552\pi\)
\(110\) −3.15168 + 17.8741i −0.300501 + 1.70422i
\(111\) 0 0
\(112\) 12.8036 3.19309i 1.20983 0.301718i
\(113\) −1.98832 0.723688i −0.187045 0.0680789i 0.246799 0.969067i \(-0.420621\pi\)
−0.433845 + 0.900988i \(0.642843\pi\)
\(114\) 0 0
\(115\) 17.8113 + 14.9454i 1.66091 + 1.39367i
\(116\) 0.0732182 + 0.126818i 0.00679814 + 0.0117747i
\(117\) 0 0
\(118\) 3.20132 + 5.54485i 0.294705 + 0.510445i
\(119\) 1.09267 1.50411i 0.100165 0.137882i
\(120\) 0 0
\(121\) 4.60286 + 1.67530i 0.418442 + 0.152300i
\(122\) 0.0668330 + 0.379029i 0.00605077 + 0.0343156i
\(123\) 0 0
\(124\) −3.94816 3.31290i −0.354555 0.297507i
\(125\) −15.3076 26.5135i −1.36915 2.37144i
\(126\) 0 0
\(127\) −5.21371 + 9.03041i −0.462642 + 0.801320i −0.999092 0.0426127i \(-0.986432\pi\)
0.536450 + 0.843932i \(0.319765\pi\)
\(128\) 10.6182 3.86470i 0.938524 0.341595i
\(129\) 0 0
\(130\) −0.794717 + 0.666847i −0.0697013 + 0.0584864i
\(131\) −4.62719 + 3.88267i −0.404279 + 0.339231i −0.822145 0.569278i \(-0.807223\pi\)
0.417866 + 0.908509i \(0.362778\pi\)
\(132\) 0 0
\(133\) −10.0532 + 13.8387i −0.871720 + 1.19997i
\(134\) −27.0678 −2.33831
\(135\) 0 0
\(136\) 0.550560 0.953598i 0.0472101 0.0817703i
\(137\) −2.40899 + 0.876802i −0.205814 + 0.0749103i −0.442870 0.896586i \(-0.646040\pi\)
0.237056 + 0.971496i \(0.423818\pi\)
\(138\) 0 0
\(139\) −0.548284 3.10947i −0.0465048 0.263742i 0.952686 0.303955i \(-0.0983074\pi\)
−0.999191 + 0.0402133i \(0.987196\pi\)
\(140\) 8.51069 + 8.81205i 0.719284 + 0.744754i
\(141\) 0 0
\(142\) −23.3413 + 8.49553i −1.95876 + 0.712929i
\(143\) −0.174386 0.302045i −0.0145829 0.0252582i
\(144\) 0 0
\(145\) 0.274347 0.475182i 0.0227832 0.0394617i
\(146\) 21.0970 7.67868i 1.74600 0.635492i
\(147\) 0 0
\(148\) 0.660728 0.554417i 0.0543115 0.0455728i
\(149\) −11.8471 4.31199i −0.970551 0.353252i −0.192392 0.981318i \(-0.561624\pi\)
−0.778160 + 0.628066i \(0.783847\pi\)
\(150\) 0 0
\(151\) 2.81699 15.9759i 0.229243 1.30010i −0.625162 0.780495i \(-0.714967\pi\)
0.854405 0.519607i \(-0.173922\pi\)
\(152\) −5.06546 + 8.77363i −0.410863 + 0.711635i
\(153\) 0 0
\(154\) −9.55715 + 6.44719i −0.770137 + 0.519529i
\(155\) −3.35345 + 19.0184i −0.269356 + 1.52759i
\(156\) 0 0
\(157\) 6.45448 5.41595i 0.515124 0.432240i −0.347804 0.937567i \(-0.613073\pi\)
0.862928 + 0.505327i \(0.168628\pi\)
\(158\) 9.56104 + 3.47994i 0.760636 + 0.276849i
\(159\) 0 0
\(160\) 18.0725 + 15.1646i 1.42875 + 1.19887i
\(161\) 1.03106 + 14.7326i 0.0812590 + 1.16109i
\(162\) 0 0
\(163\) 4.06419 + 7.03938i 0.318332 + 0.551367i 0.980140 0.198306i \(-0.0635440\pi\)
−0.661808 + 0.749673i \(0.730211\pi\)
\(164\) −3.43785 + 1.25128i −0.268451 + 0.0977083i
\(165\) 0 0
\(166\) −3.25169 + 2.72849i −0.252380 + 0.211772i
\(167\) 18.8324 + 6.85444i 1.45730 + 0.530412i 0.944619 0.328169i \(-0.106432\pi\)
0.512677 + 0.858582i \(0.328654\pi\)
\(168\) 0 0
\(169\) −2.25396 + 12.7829i −0.173382 + 0.983298i
\(170\) 5.16299 0.395983
\(171\) 0 0
\(172\) 6.69782 0.510704
\(173\) 19.8173 + 16.6287i 1.50668 + 1.26426i 0.869913 + 0.493206i \(0.164175\pi\)
0.636772 + 0.771052i \(0.280269\pi\)
\(174\) 0 0
\(175\) 9.00463 31.4097i 0.680686 2.37435i
\(176\) −9.43771 + 7.91918i −0.711394 + 0.596931i
\(177\) 0 0
\(178\) 0.276962 1.57073i 0.0207592 0.117731i
\(179\) −19.5468 −1.46100 −0.730499 0.682914i \(-0.760712\pi\)
−0.730499 + 0.682914i \(0.760712\pi\)
\(180\) 0 0
\(181\) 1.41161 2.44499i 0.104924 0.181734i −0.808783 0.588107i \(-0.799873\pi\)
0.913707 + 0.406373i \(0.133207\pi\)
\(182\) −0.655353 0.0688420i −0.0485780 0.00510291i
\(183\) 0 0
\(184\) 1.51894 + 8.61434i 0.111978 + 0.635057i
\(185\) −3.03694 1.10535i −0.223280 0.0812673i
\(186\) 0 0
\(187\) −0.301407 + 1.70936i −0.0220410 + 0.125001i
\(188\) 6.61690 0.482587
\(189\) 0 0
\(190\) −47.5023 −3.44618
\(191\) 1.41634 8.03246i 0.102483 0.581208i −0.889713 0.456520i \(-0.849096\pi\)
0.992196 0.124688i \(-0.0397931\pi\)
\(192\) 0 0
\(193\) −2.78662 1.01425i −0.200585 0.0730071i 0.239774 0.970829i \(-0.422927\pi\)
−0.440359 + 0.897822i \(0.645149\pi\)
\(194\) −0.564196 3.19972i −0.0405069 0.229726i
\(195\) 0 0
\(196\) −0.270672 + 7.77685i −0.0193337 + 0.555489i
\(197\) 8.95897 15.5174i 0.638300 1.10557i −0.347505 0.937678i \(-0.612971\pi\)
0.985806 0.167891i \(-0.0536955\pi\)
\(198\) 0 0
\(199\) 11.7675 0.834176 0.417088 0.908866i \(-0.363051\pi\)
0.417088 + 0.908866i \(0.363051\pi\)
\(200\) 3.36059 19.0588i 0.237629 1.34766i
\(201\) 0 0
\(202\) −10.9916 + 9.22309i −0.773370 + 0.648934i
\(203\) 0.338164 0.0843345i 0.0237344 0.00591912i
\(204\) 0 0
\(205\) 10.5011 + 8.81150i 0.733431 + 0.615422i
\(206\) 11.2997 0.787287
\(207\) 0 0
\(208\) −0.704206 −0.0488279
\(209\) 2.77311 15.7271i 0.191820 1.08786i
\(210\) 0 0
\(211\) 4.57923 + 1.66670i 0.315247 + 0.114741i 0.494798 0.869008i \(-0.335242\pi\)
−0.179550 + 0.983749i \(0.557464\pi\)
\(212\) 3.16772 2.65804i 0.217560 0.182555i
\(213\) 0 0
\(214\) −19.7795 + 7.19914i −1.35210 + 0.492123i
\(215\) −12.5483 21.7343i −0.855786 1.48226i
\(216\) 0 0
\(217\) −10.1690 + 6.85994i −0.690317 + 0.465683i
\(218\) −0.433042 0.363365i −0.0293293 0.0246102i
\(219\) 0 0
\(220\) −10.7481 3.91198i −0.724635 0.263746i
\(221\) −0.0760018 + 0.0637730i −0.00511243 + 0.00428984i
\(222\) 0 0
\(223\) 3.39420 19.2495i 0.227292 1.28904i −0.630962 0.775814i \(-0.717339\pi\)
0.858254 0.513225i \(-0.171549\pi\)
\(224\) 1.04618 + 14.9486i 0.0699009 + 0.998798i
\(225\) 0 0
\(226\) 1.86623 3.23241i 0.124140 0.215017i
\(227\) 2.13798 12.1251i 0.141902 0.804769i −0.827900 0.560876i \(-0.810464\pi\)
0.969802 0.243893i \(-0.0784245\pi\)
\(228\) 0 0
\(229\) 24.0912 + 8.76849i 1.59199 + 0.579438i 0.977767 0.209693i \(-0.0672465\pi\)
0.614225 + 0.789131i \(0.289469\pi\)
\(230\) −31.4189 + 26.3636i −2.07170 + 1.73836i
\(231\) 0 0
\(232\) 0.193975 0.0706009i 0.0127351 0.00463518i
\(233\) 3.66677 6.35103i 0.240218 0.416070i −0.720558 0.693395i \(-0.756114\pi\)
0.960776 + 0.277324i \(0.0894477\pi\)
\(234\) 0 0
\(235\) −12.3967 21.4717i −0.808670 1.40066i
\(236\) −3.79156 + 1.38002i −0.246810 + 0.0898314i
\(237\) 0 0
\(238\) 2.27823 + 2.35890i 0.147676 + 0.152905i
\(239\) −2.57748 14.6176i −0.166723 0.945536i −0.947270 0.320438i \(-0.896170\pi\)
0.780546 0.625098i \(-0.214941\pi\)
\(240\) 0 0
\(241\) 16.4437 5.98501i 1.05923 0.385529i 0.247092 0.968992i \(-0.420525\pi\)
0.812139 + 0.583464i \(0.198303\pi\)
\(242\) −4.32024 + 7.48287i −0.277715 + 0.481017i
\(243\) 0 0
\(244\) −0.242546 −0.0155274
\(245\) 25.7428 13.6915i 1.64465 0.874719i
\(246\) 0 0
\(247\) 0.699258 0.586747i 0.0444927 0.0373338i
\(248\) −5.56551 + 4.67002i −0.353410 + 0.296546i
\(249\) 0 0
\(250\) 50.7478 18.4707i 3.20957 1.16819i
\(251\) 6.62373 11.4726i 0.418086 0.724147i −0.577661 0.816277i \(-0.696034\pi\)
0.995747 + 0.0921303i \(0.0293676\pi\)
\(252\) 0 0
\(253\) −6.89427 11.9412i −0.433439 0.750738i
\(254\) −14.0905 11.8233i −0.884117 0.741862i
\(255\) 0 0
\(256\) 3.46676 + 19.6610i 0.216673 + 1.22881i
\(257\) −20.3970 7.42389i −1.27233 0.463090i −0.384441 0.923150i \(-0.625606\pi\)
−0.887888 + 0.460060i \(0.847828\pi\)
\(258\) 0 0
\(259\) −0.835063 1.87529i −0.0518883 0.116525i
\(260\) −0.326890 0.566191i −0.0202729 0.0351136i
\(261\) 0 0
\(262\) −5.32756 9.22761i −0.329138 0.570084i
\(263\) −8.30629 6.96981i −0.512188 0.429777i 0.349710 0.936858i \(-0.386280\pi\)
−0.861898 + 0.507081i \(0.830724\pi\)
\(264\) 0 0
\(265\) −14.5599 5.29939i −0.894410 0.325539i
\(266\) −20.9610 21.7032i −1.28520 1.33071i
\(267\) 0 0
\(268\) 2.96208 16.7988i 0.180938 1.02615i
\(269\) 6.69178 11.5905i 0.408005 0.706686i −0.586661 0.809833i \(-0.699558\pi\)
0.994666 + 0.103147i \(0.0328911\pi\)
\(270\) 0 0
\(271\) 10.7152 + 18.5593i 0.650904 + 1.12740i 0.982904 + 0.184120i \(0.0589433\pi\)
−0.332000 + 0.943279i \(0.607723\pi\)
\(272\) 2.68470 + 2.25273i 0.162784 + 0.136592i
\(273\) 0 0
\(274\) −0.785264 4.45345i −0.0474395 0.269043i
\(275\) 5.29741 + 30.0431i 0.319446 + 1.81167i
\(276\) 0 0
\(277\) 4.19055 + 3.51628i 0.251785 + 0.211273i 0.759941 0.649992i \(-0.225228\pi\)
−0.508155 + 0.861265i \(0.669672\pi\)
\(278\) 5.56969 0.334048
\(279\) 0 0
\(280\) 14.3164 9.65776i 0.855570 0.577161i
\(281\) −13.4765 + 4.90506i −0.803942 + 0.292611i −0.711119 0.703072i \(-0.751811\pi\)
−0.0928232 + 0.995683i \(0.529589\pi\)
\(282\) 0 0
\(283\) −1.38317 7.84435i −0.0822209 0.466298i −0.997922 0.0644373i \(-0.979475\pi\)
0.915701 0.401861i \(-0.131636\pi\)
\(284\) −2.71821 15.4157i −0.161296 0.914754i
\(285\) 0 0
\(286\) 0.578125 0.210420i 0.0341853 0.0124424i
\(287\) 0.607891 + 8.68602i 0.0358827 + 0.512720i
\(288\) 0 0
\(289\) −16.5062 −0.970956
\(290\) 0.741445 + 0.622146i 0.0435392 + 0.0365337i
\(291\) 0 0
\(292\) 2.45685 + 13.9335i 0.143776 + 0.815396i
\(293\) −3.09426 17.5484i −0.180768 1.02519i −0.931273 0.364323i \(-0.881300\pi\)
0.750504 0.660866i \(-0.229811\pi\)
\(294\) 0 0
\(295\) 11.5816 + 9.71809i 0.674305 + 0.565809i
\(296\) −0.607924 1.05295i −0.0353348 0.0612018i
\(297\) 0 0
\(298\) 11.1197 19.2598i 0.644144 1.11569i
\(299\) 0.136860 0.776170i 0.00791480 0.0448871i
\(300\) 0 0
\(301\) 4.39303 15.3237i 0.253210 0.883241i
\(302\) 26.8903 + 9.78727i 1.54736 + 0.563194i
\(303\) 0 0
\(304\) −24.7007 20.7264i −1.41668 1.18874i
\(305\) 0.454406 + 0.787055i 0.0260192 + 0.0450666i
\(306\) 0 0
\(307\) −0.753447 1.30501i −0.0430015 0.0744808i 0.843724 0.536778i \(-0.180359\pi\)
−0.886725 + 0.462297i \(0.847025\pi\)
\(308\) −2.95539 6.63687i −0.168399 0.378171i
\(309\) 0 0
\(310\) −32.0113 11.6511i −1.81812 0.661741i
\(311\) 1.01822 + 5.77462i 0.0577380 + 0.327449i 0.999972 0.00750727i \(-0.00238966\pi\)
−0.942234 + 0.334956i \(0.891279\pi\)
\(312\) 0 0
\(313\) −1.42966 1.19963i −0.0808090 0.0678068i 0.601488 0.798882i \(-0.294575\pi\)
−0.682297 + 0.731075i \(0.739019\pi\)
\(314\) 7.43144 + 12.8716i 0.419380 + 0.726388i
\(315\) 0 0
\(316\) −3.20599 + 5.55294i −0.180351 + 0.312378i
\(317\) −9.31341 + 3.38980i −0.523093 + 0.190390i −0.590052 0.807365i \(-0.700893\pi\)
0.0669586 + 0.997756i \(0.478670\pi\)
\(318\) 0 0
\(319\) −0.249265 + 0.209158i −0.0139561 + 0.0117106i
\(320\) −0.0508601 + 0.0426767i −0.00284316 + 0.00238570i
\(321\) 0 0
\(322\) −25.9091 2.72164i −1.44386 0.151671i
\(323\) −4.54282 −0.252769
\(324\) 0 0
\(325\) −0.871867 + 1.51012i −0.0483625 + 0.0837662i
\(326\) −13.4737 + 4.90401i −0.746236 + 0.271608i
\(327\) 0 0
\(328\) 0.895534 + 5.07882i 0.0494476 + 0.280431i
\(329\) 4.33995 15.1385i 0.239269 0.834614i
\(330\) 0 0
\(331\) −9.12572 + 3.32149i −0.501595 + 0.182566i −0.580411 0.814324i \(-0.697108\pi\)
0.0788163 + 0.996889i \(0.474886\pi\)
\(332\) −1.33752 2.31664i −0.0734057 0.127142i
\(333\) 0 0
\(334\) −17.6761 + 30.6159i −0.967192 + 1.67522i
\(335\) −60.0611 + 21.8605i −3.28149 + 1.19436i
\(336\) 0 0
\(337\) −16.7483 + 14.0535i −0.912339 + 0.765543i −0.972562 0.232642i \(-0.925263\pi\)
0.0602239 + 0.998185i \(0.480819\pi\)
\(338\) −21.5158 7.83112i −1.17031 0.425957i
\(339\) 0 0
\(340\) −0.564995 + 3.20424i −0.0306411 + 0.173775i
\(341\) 5.72623 9.91812i 0.310093 0.537096i
\(342\) 0 0
\(343\) 17.6148 + 5.72001i 0.951110 + 0.308852i
\(344\) 1.63951 9.29812i 0.0883964 0.501321i
\(345\) 0 0
\(346\) −34.9575 + 29.3329i −1.87933 + 1.57694i
\(347\) 9.34786 + 3.40234i 0.501819 + 0.182647i 0.580512 0.814252i \(-0.302852\pi\)
−0.0786928 + 0.996899i \(0.525075\pi\)
\(348\) 0 0
\(349\) −19.2188 16.1265i −1.02876 0.863233i −0.0380577 0.999276i \(-0.512117\pi\)
−0.990703 + 0.136043i \(0.956562\pi\)
\(350\) 51.8064 + 25.2639i 2.76917 + 1.35041i
\(351\) 0 0
\(352\) −6.99537 12.1163i −0.372854 0.645803i
\(353\) −9.30697 + 3.38746i −0.495360 + 0.180296i −0.577606 0.816316i \(-0.696013\pi\)
0.0822460 + 0.996612i \(0.473791\pi\)
\(354\) 0 0
\(355\) −44.9311 + 37.7016i −2.38469 + 2.00100i
\(356\) 0.944515 + 0.343775i 0.0500592 + 0.0182201i
\(357\) 0 0
\(358\) 5.98745 33.9565i 0.316447 1.79466i
\(359\) 16.5248 0.872144 0.436072 0.899912i \(-0.356369\pi\)
0.436072 + 0.899912i \(0.356369\pi\)
\(360\) 0 0
\(361\) 22.7965 1.19981
\(362\) 3.81501 + 3.20117i 0.200512 + 0.168250i
\(363\) 0 0
\(364\) 0.114441 0.399191i 0.00599834 0.0209233i
\(365\) 40.6109 34.0766i 2.12567 1.78365i
\(366\) 0 0
\(367\) −5.50999 + 31.2487i −0.287619 + 1.63117i 0.408157 + 0.912912i \(0.366172\pi\)
−0.695776 + 0.718259i \(0.744939\pi\)
\(368\) −27.8405 −1.45129
\(369\) 0 0
\(370\) 2.85046 4.93715i 0.148188 0.256670i
\(371\) −4.00353 8.99068i −0.207853 0.466773i
\(372\) 0 0
\(373\) −4.16072 23.5966i −0.215434 1.22179i −0.880152 0.474692i \(-0.842559\pi\)
0.664718 0.747094i \(-0.268552\pi\)
\(374\) −2.87716 1.04720i −0.148774 0.0541494i
\(375\) 0 0
\(376\) 1.61970 9.18578i 0.0835296 0.473720i
\(377\) −0.0185992 −0.000957907
\(378\) 0 0
\(379\) 18.5458 0.952632 0.476316 0.879274i \(-0.341972\pi\)
0.476316 + 0.879274i \(0.341972\pi\)
\(380\) 5.19826 29.4808i 0.266665 1.51233i
\(381\) 0 0
\(382\) 13.5200 + 4.92090i 0.691746 + 0.251775i
\(383\) 3.93094 + 22.2935i 0.200862 + 1.13914i 0.903820 + 0.427912i \(0.140751\pi\)
−0.702959 + 0.711231i \(0.748138\pi\)
\(384\) 0 0
\(385\) −15.9996 + 22.0243i −0.815416 + 1.12246i
\(386\) 2.61552 4.53021i 0.133126 0.230581i
\(387\) 0 0
\(388\) 2.04754 0.103948
\(389\) −1.59902 + 9.06849i −0.0810735 + 0.459791i 0.917061 + 0.398746i \(0.130554\pi\)
−0.998135 + 0.0610450i \(0.980557\pi\)
\(390\) 0 0
\(391\) −3.00470 + 2.52124i −0.151954 + 0.127505i
\(392\) 10.7298 + 2.27939i 0.541937 + 0.115127i
\(393\) 0 0
\(394\) 24.2124 + 20.3166i 1.21980 + 1.02354i
\(395\) 24.0256 1.20886
\(396\) 0 0
\(397\) −16.3534 −0.820753 −0.410376 0.911916i \(-0.634603\pi\)
−0.410376 + 0.911916i \(0.634603\pi\)
\(398\) −3.60454 + 20.4424i −0.180679 + 1.02468i
\(399\) 0 0
\(400\) 57.8813 + 21.0671i 2.89406 + 1.05335i
\(401\) −28.0881 + 23.5687i −1.40265 + 1.17697i −0.442748 + 0.896646i \(0.645997\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(402\) 0 0
\(403\) 0.615137 0.223891i 0.0306421 0.0111528i
\(404\) −4.52118 7.83092i −0.224937 0.389603i
\(405\) 0 0
\(406\) 0.0429209 + 0.613287i 0.00213013 + 0.0304369i
\(407\) 1.46819 + 1.23195i 0.0727753 + 0.0610657i
\(408\) 0 0
\(409\) −1.51858 0.552719i −0.0750891 0.0273302i 0.304203 0.952607i \(-0.401610\pi\)
−0.379292 + 0.925277i \(0.623832\pi\)
\(410\) −18.5239 + 15.5434i −0.914829 + 0.767633i
\(411\) 0 0
\(412\) −1.23655 + 7.01280i −0.0609203 + 0.345496i
\(413\) 0.670435 + 9.57970i 0.0329900 + 0.471386i
\(414\) 0 0
\(415\) −5.01164 + 8.68041i −0.246012 + 0.426104i
\(416\) 0.138867 0.787552i 0.00680849 0.0386129i
\(417\) 0 0
\(418\) 26.4715 + 9.63482i 1.29476 + 0.471255i
\(419\) −11.2741 + 9.46013i −0.550778 + 0.462158i −0.875204 0.483753i \(-0.839273\pi\)
0.324426 + 0.945911i \(0.394829\pi\)
\(420\) 0 0
\(421\) 12.7240 4.63116i 0.620130 0.225709i −0.0127998 0.999918i \(-0.504074\pi\)
0.632930 + 0.774209i \(0.281852\pi\)
\(422\) −4.29806 + 7.44446i −0.209226 + 0.362390i
\(423\) 0 0
\(424\) −2.91456 5.04817i −0.141544 0.245161i
\(425\) 8.15470 2.96807i 0.395561 0.143972i
\(426\) 0 0
\(427\) −0.159083 + 0.554910i −0.00769858 + 0.0268540i
\(428\) −2.30342 13.0633i −0.111340 0.631440i
\(429\) 0 0
\(430\) 41.6002 15.1412i 2.00614 0.730176i
\(431\) 10.9091 18.8951i 0.525472 0.910145i −0.474088 0.880478i \(-0.657222\pi\)
0.999560 0.0296670i \(-0.00944470\pi\)
\(432\) 0 0
\(433\) 10.1358 0.487096 0.243548 0.969889i \(-0.421689\pi\)
0.243548 + 0.969889i \(0.421689\pi\)
\(434\) −8.80210 19.7668i −0.422514 0.948835i
\(435\) 0 0
\(436\) 0.272900 0.228990i 0.0130695 0.0109666i
\(437\) 27.6449 23.1968i 1.32244 1.10966i
\(438\) 0 0
\(439\) −2.67426 + 0.973350i −0.127635 + 0.0464554i −0.405048 0.914295i \(-0.632745\pi\)
0.277413 + 0.960751i \(0.410523\pi\)
\(440\) −8.06167 + 13.9632i −0.384325 + 0.665671i
\(441\) 0 0
\(442\) −0.0875055 0.151564i −0.00416221 0.00720916i
\(443\) 4.88441 + 4.09850i 0.232065 + 0.194726i 0.751404 0.659843i \(-0.229377\pi\)
−0.519339 + 0.854569i \(0.673822\pi\)
\(444\) 0 0
\(445\) −0.653995 3.70899i −0.0310023 0.175823i
\(446\) 32.4003 + 11.7927i 1.53420 + 0.558402i
\(447\) 0 0
\(448\) −0.0419411 0.00440573i −0.00198153 0.000208151i
\(449\) 2.33757 + 4.04880i 0.110317 + 0.191074i 0.915898 0.401411i \(-0.131480\pi\)
−0.805581 + 0.592485i \(0.798147\pi\)
\(450\) 0 0
\(451\) −4.06471 7.04029i −0.191400 0.331514i
\(452\) 1.80187 + 1.51195i 0.0847527 + 0.0711159i
\(453\) 0 0
\(454\) 20.4086 + 7.42813i 0.957824 + 0.348620i
\(455\) −1.50977 + 0.376520i −0.0707790 + 0.0176515i
\(456\) 0 0
\(457\) 3.33384 18.9071i 0.155950 0.884438i −0.801962 0.597375i \(-0.796210\pi\)
0.957912 0.287062i \(-0.0926787\pi\)
\(458\) −22.6120 + 39.1651i −1.05659 + 1.83006i
\(459\) 0 0
\(460\) −12.9235 22.3841i −0.602561 1.04367i
\(461\) 1.41824 + 1.19004i 0.0660540 + 0.0554259i 0.675217 0.737619i \(-0.264050\pi\)
−0.609163 + 0.793045i \(0.708494\pi\)
\(462\) 0 0
\(463\) −2.62612 14.8935i −0.122046 0.692158i −0.983019 0.183506i \(-0.941255\pi\)
0.860972 0.508652i \(-0.169856\pi\)
\(464\) 0.114087 + 0.647020i 0.00529636 + 0.0300371i
\(465\) 0 0
\(466\) 9.90976 + 8.31528i 0.459061 + 0.385198i
\(467\) 24.7350 1.14460 0.572300 0.820044i \(-0.306051\pi\)
0.572300 + 0.820044i \(0.306051\pi\)
\(468\) 0 0
\(469\) −36.4905 17.7950i −1.68497 0.821696i
\(470\) 41.0976 14.9583i 1.89569 0.689975i
\(471\) 0 0
\(472\) 0.987672 + 5.60137i 0.0454613 + 0.257824i
\(473\) 2.58441 + 14.6569i 0.118831 + 0.673926i
\(474\) 0 0
\(475\) −75.0277 + 27.3079i −3.44251 + 1.25297i
\(476\) −1.71329 + 1.15577i −0.0785285 + 0.0529748i
\(477\) 0 0
\(478\) 26.1831 1.19759
\(479\) −24.2765 20.3704i −1.10922 0.930748i −0.111211 0.993797i \(-0.535473\pi\)
−0.998010 + 0.0630491i \(0.979918\pi\)
\(480\) 0 0
\(481\) 0.0190232 + 0.107886i 0.000867385 + 0.00491918i
\(482\) 5.36018 + 30.3991i 0.244149 + 1.38464i
\(483\) 0 0
\(484\) −4.17124 3.50008i −0.189602 0.159095i
\(485\) −3.83605 6.64423i −0.174186 0.301699i
\(486\) 0 0
\(487\) 15.0234 26.0213i 0.680775 1.17914i −0.293969 0.955815i \(-0.594976\pi\)
0.974745 0.223323i \(-0.0716904\pi\)
\(488\) −0.0593709 + 0.336709i −0.00268760 + 0.0152421i
\(489\) 0 0
\(490\) 15.8994 + 48.9140i 0.718261 + 2.20971i
\(491\) −29.0255 10.5644i −1.30990 0.476766i −0.409695 0.912223i \(-0.634365\pi\)
−0.900210 + 0.435456i \(0.856587\pi\)
\(492\) 0 0
\(493\) 0.0709071 + 0.0594981i 0.00319350 + 0.00267966i
\(494\) 0.805098 + 1.39447i 0.0362231 + 0.0627402i
\(495\) 0 0
\(496\) −11.5619 20.0257i −0.519143 0.899182i
\(497\) −37.0518 3.89213i −1.66200 0.174586i
\(498\) 0 0
\(499\) −14.5259 5.28698i −0.650267 0.236678i −0.00423824 0.999991i \(-0.501349\pi\)
−0.646029 + 0.763313i \(0.723571\pi\)
\(500\) 5.90983 + 33.5163i 0.264295 + 1.49889i
\(501\) 0 0
\(502\) 17.9012 + 15.0209i 0.798970 + 0.670415i
\(503\) 12.4023 + 21.4813i 0.552989 + 0.957806i 0.998057 + 0.0623088i \(0.0198464\pi\)
−0.445067 + 0.895497i \(0.646820\pi\)
\(504\) 0 0
\(505\) −16.9408 + 29.3423i −0.753854 + 1.30571i
\(506\) 22.8560 8.31889i 1.01607 0.369820i
\(507\) 0 0
\(508\) 8.87973 7.45098i 0.393974 0.330584i
\(509\) −1.04593 + 0.877641i −0.0463601 + 0.0389008i −0.665673 0.746243i \(-0.731856\pi\)
0.619313 + 0.785144i \(0.287411\pi\)
\(510\) 0 0
\(511\) 33.4893 + 3.51790i 1.48148 + 0.155623i
\(512\) −12.6175 −0.557620
\(513\) 0 0
\(514\) 19.1446 33.1594i 0.844430 1.46260i
\(515\) 25.0730 9.12584i 1.10485 0.402132i
\(516\) 0 0
\(517\) 2.55319 + 14.4798i 0.112289 + 0.636823i
\(518\) 3.51352 0.876236i 0.154375 0.0384996i
\(519\) 0 0
\(520\) −0.866020 + 0.315205i −0.0379775 + 0.0138227i
\(521\) −13.2774 22.9971i −0.581693 1.00752i −0.995279 0.0970569i \(-0.969057\pi\)
0.413586 0.910465i \(-0.364276\pi\)
\(522\) 0 0
\(523\) 17.0005 29.4458i 0.743381 1.28757i −0.207566 0.978221i \(-0.566554\pi\)
0.950947 0.309353i \(-0.100113\pi\)
\(524\) 6.30983 2.29659i 0.275646 0.100327i
\(525\) 0 0
\(526\) 14.6522 12.2947i 0.638866 0.536072i
\(527\) −3.06136 1.11424i −0.133355 0.0485372i
\(528\) 0 0
\(529\) 1.41679 8.03502i 0.0615996 0.349349i
\(530\) 13.6659 23.6701i 0.593610 1.02816i
\(531\) 0 0
\(532\) 15.7632 10.6337i 0.683422 0.461032i
\(533\) 0.0806895 0.457613i 0.00349505 0.0198214i
\(534\) 0 0
\(535\) −38.0748 + 31.9485i −1.64612 + 1.38125i
\(536\) −22.5955 8.22410i −0.975979 0.355227i
\(537\) 0 0
\(538\) 18.0851 + 15.1752i 0.779705 + 0.654250i
\(539\) −17.1226 + 2.40845i −0.737524 + 0.103739i
\(540\) 0 0
\(541\) −1.17215 2.03023i −0.0503948 0.0872863i 0.839728 0.543008i \(-0.182715\pi\)
−0.890122 + 0.455722i \(0.849381\pi\)
\(542\) −35.5233 + 12.9294i −1.52586 + 0.555366i
\(543\) 0 0
\(544\) −3.04876 + 2.55822i −0.130715 + 0.109683i
\(545\) −1.25434 0.456543i −0.0537300 0.0195561i
\(546\) 0 0
\(547\) 3.75899 21.3183i 0.160723 0.911504i −0.792643 0.609686i \(-0.791296\pi\)
0.953366 0.301818i \(-0.0975934\pi\)
\(548\) 2.84983 0.121739
\(549\) 0 0
\(550\) −53.8132 −2.29460
\(551\) −0.652385 0.547416i −0.0277925 0.0233207i
\(552\) 0 0
\(553\) 10.6016 + 10.9770i 0.450825 + 0.466789i
\(554\) −7.39207 + 6.20268i −0.314059 + 0.263527i
\(555\) 0 0
\(556\) −0.609501 + 3.45665i −0.0258486 + 0.146595i
\(557\) 9.14873 0.387644 0.193822 0.981037i \(-0.437912\pi\)
0.193822 + 0.981037i \(0.437912\pi\)
\(558\) 0 0
\(559\) −0.425352 + 0.736731i −0.0179905 + 0.0311604i
\(560\) 22.3591 + 50.2115i 0.944844 + 2.12182i
\(561\) 0 0
\(562\) −4.39297 24.9138i −0.185306 1.05092i
\(563\) 31.8857 + 11.6055i 1.34382 + 0.489111i 0.911014 0.412374i \(-0.135300\pi\)
0.432808 + 0.901486i \(0.357523\pi\)
\(564\) 0 0
\(565\) 1.53045 8.67962i 0.0643866 0.365155i
\(566\) 14.0508 0.590599
\(567\) 0 0
\(568\) −22.0659 −0.925866
\(569\) −3.23972 + 18.3734i −0.135816 + 0.770251i 0.838472 + 0.544945i \(0.183449\pi\)
−0.974288 + 0.225306i \(0.927662\pi\)
\(570\) 0 0
\(571\) −3.69402 1.34451i −0.154590 0.0562661i 0.263566 0.964641i \(-0.415101\pi\)
−0.418156 + 0.908375i \(0.637323\pi\)
\(572\) 0.0673255 + 0.381822i 0.00281502 + 0.0159648i
\(573\) 0 0
\(574\) −15.2755 1.60462i −0.637585 0.0669756i
\(575\) −34.4689 + 59.7019i −1.43745 + 2.48974i
\(576\) 0 0
\(577\) 7.95004 0.330965 0.165482 0.986213i \(-0.447082\pi\)
0.165482 + 0.986213i \(0.447082\pi\)
\(578\) 5.05608 28.6745i 0.210305 1.19270i
\(579\) 0 0
\(580\) −0.467253 + 0.392072i −0.0194016 + 0.0162799i
\(581\) −6.17742 + 1.54058i −0.256282 + 0.0639141i
\(582\) 0 0
\(583\) 7.03891 + 5.90634i 0.291522 + 0.244616i
\(584\) 19.9443 0.825300
\(585\) 0 0
\(586\) 31.4327 1.29847
\(587\) 3.92585 22.2646i 0.162037 0.918958i −0.790030 0.613068i \(-0.789935\pi\)
0.952067 0.305890i \(-0.0989538\pi\)
\(588\) 0 0
\(589\) 28.1662 + 10.2516i 1.16057 + 0.422412i
\(590\) −20.4297 + 17.1426i −0.841079 + 0.705749i
\(591\) 0 0
\(592\) 3.63640 1.32354i 0.149455 0.0543973i
\(593\) 11.6835 + 20.2365i 0.479785 + 0.831011i 0.999731 0.0231874i \(-0.00738143\pi\)
−0.519946 + 0.854199i \(0.674048\pi\)
\(594\) 0 0
\(595\) 6.96028 + 3.39426i 0.285344 + 0.139151i
\(596\) 10.7361 + 9.00870i 0.439770 + 0.369011i
\(597\) 0 0
\(598\) 1.30643 + 0.475502i 0.0534240 + 0.0194447i
\(599\) 25.1192 21.0775i 1.02634 0.861204i 0.0359318 0.999354i \(-0.488560\pi\)
0.990411 + 0.138150i \(0.0441156\pi\)
\(600\) 0 0
\(601\) 6.43928 36.5190i 0.262664 1.48964i −0.512943 0.858423i \(-0.671445\pi\)
0.775606 0.631217i \(-0.217444\pi\)
\(602\) 25.2745 + 12.3254i 1.03011 + 0.502344i
\(603\) 0 0
\(604\) −9.01681 + 15.6176i −0.366889 + 0.635470i
\(605\) −3.54292 + 20.0929i −0.144040 + 0.816893i
\(606\) 0 0
\(607\) −14.1208 5.13953i −0.573144 0.208607i 0.0391558 0.999233i \(-0.487533\pi\)
−0.612300 + 0.790626i \(0.709755\pi\)
\(608\) 28.0503 23.5370i 1.13759 0.954551i
\(609\) 0 0
\(610\) −1.50645 + 0.548304i −0.0609945 + 0.0222002i
\(611\) −0.420213 + 0.727830i −0.0170000 + 0.0294449i
\(612\) 0 0
\(613\) 14.0661 + 24.3632i 0.568125 + 0.984021i 0.996751 + 0.0805393i \(0.0256643\pi\)
−0.428627 + 0.903482i \(0.641002\pi\)
\(614\) 2.49784 0.909139i 0.100805 0.0366899i
\(615\) 0 0
\(616\) −9.93693 + 2.47817i −0.400370 + 0.0998482i
\(617\) −0.135031 0.765797i −0.00543613 0.0308298i 0.981969 0.189042i \(-0.0605382\pi\)
−0.987405 + 0.158212i \(0.949427\pi\)
\(618\) 0 0
\(619\) 10.3239 3.75760i 0.414953 0.151031i −0.126103 0.992017i \(-0.540247\pi\)
0.541056 + 0.840987i \(0.318025\pi\)
\(620\) 10.7340 18.5918i 0.431087 0.746664i
\(621\) 0 0
\(622\) −10.3435 −0.414737
\(623\) 1.40601 1.93544i 0.0563305 0.0775417i
\(624\) 0 0
\(625\) 50.3844 42.2775i 2.01538 1.69110i
\(626\) 2.52190 2.11612i 0.100795 0.0845773i
\(627\) 0 0
\(628\) −8.80160 + 3.20352i −0.351222 + 0.127834i
\(629\) 0.272600 0.472157i 0.0108693 0.0188262i
\(630\) 0 0
\(631\) 21.9799 + 38.0704i 0.875008 + 1.51556i 0.856755 + 0.515724i \(0.172477\pi\)
0.0182532 + 0.999833i \(0.494190\pi\)
\(632\) 6.92399 + 5.80992i 0.275422 + 0.231106i
\(633\) 0 0
\(634\) −3.03591 17.2175i −0.120571 0.683794i
\(635\) −40.8143 14.8552i −1.61967 0.589510i
\(636\) 0 0
\(637\) −0.838231 0.523650i −0.0332119 0.0207478i
\(638\) −0.286994 0.497088i −0.0113622 0.0196799i
\(639\) 0 0
\(640\) 23.5334 + 40.7610i 0.930238 + 1.61122i
\(641\) 25.0939 + 21.0563i 0.991149 + 0.831673i 0.985734 0.168312i \(-0.0538317\pi\)
0.00541559 + 0.999985i \(0.498276\pi\)
\(642\) 0 0
\(643\) 15.9951 + 5.82174i 0.630785 + 0.229587i 0.637573 0.770390i \(-0.279938\pi\)
−0.00678774 + 0.999977i \(0.502161\pi\)
\(644\) 4.52439 15.7819i 0.178286 0.621892i
\(645\) 0 0
\(646\) 1.39153 7.89174i 0.0547489 0.310496i
\(647\) −14.6339 + 25.3466i −0.575317 + 0.996479i 0.420690 + 0.907205i \(0.361788\pi\)
−0.996007 + 0.0892745i \(0.971545\pi\)
\(648\) 0 0
\(649\) −4.48291 7.76464i −0.175970 0.304789i
\(650\) −2.35629 1.97717i −0.0924215 0.0775508i
\(651\) 0 0
\(652\) −1.56907 8.89865i −0.0614496 0.348498i
\(653\) −3.95607 22.4360i −0.154813 0.877988i −0.958957 0.283553i \(-0.908487\pi\)
0.804144 0.594435i \(-0.202624\pi\)
\(654\) 0 0
\(655\) −19.2738 16.1726i −0.753088 0.631916i
\(656\) −16.4142 −0.640865
\(657\) 0 0
\(658\) 24.9691 + 12.1764i 0.973396 + 0.474687i
\(659\) 1.59882 0.581922i 0.0622810 0.0226684i −0.310692 0.950511i \(-0.600561\pi\)
0.372973 + 0.927842i \(0.378338\pi\)
\(660\) 0 0
\(661\) −2.71224 15.3819i −0.105494 0.598285i −0.991022 0.133699i \(-0.957314\pi\)
0.885528 0.464586i \(-0.153797\pi\)
\(662\) −2.97473 16.8705i −0.115616 0.655691i
\(663\) 0 0
\(664\) −3.54344 + 1.28971i −0.137512 + 0.0500503i
\(665\) −64.0384 31.2290i −2.48330 1.21101i
\(666\) 0 0
\(667\) −0.735312 −0.0284714
\(668\) −17.0664 14.3204i −0.660320 0.554075i
\(669\) 0 0
\(670\) −19.5782 111.034i −0.756373 4.28960i
\(671\) −0.0935884 0.530766i −0.00361294 0.0204900i
\(672\) 0 0
\(673\) −27.8478 23.3671i −1.07346 0.900736i −0.0780940 0.996946i \(-0.524883\pi\)
−0.995361 + 0.0962102i \(0.969328\pi\)
\(674\) −19.2834 33.3997i −0.742767 1.28651i
\(675\) 0 0
\(676\) 7.21466 12.4961i 0.277487 0.480621i
\(677\) 5.55448 31.5010i 0.213476 1.21068i −0.670055 0.742311i \(-0.733730\pi\)
0.883531 0.468372i \(-0.155159\pi\)
\(678\) 0 0
\(679\) 1.34296 4.68449i 0.0515382 0.179774i
\(680\) 4.30993 + 1.56869i 0.165278 + 0.0601563i
\(681\) 0 0
\(682\) 15.4756 + 12.9856i 0.592592 + 0.497244i
\(683\) −0.740434 1.28247i −0.0283319 0.0490723i 0.851512 0.524335i \(-0.175686\pi\)
−0.879844 + 0.475263i \(0.842353\pi\)
\(684\) 0 0
\(685\) −5.33912 9.24762i −0.203997 0.353333i
\(686\) −15.3324 + 28.8481i −0.585393 + 1.10143i
\(687\) 0 0
\(688\) 28.2382 + 10.2779i 1.07657 + 0.391839i
\(689\) 0.0912029 + 0.517237i 0.00347455 + 0.0197052i
\(690\) 0 0
\(691\) 6.74135 + 5.65666i 0.256453 + 0.215190i 0.761945 0.647642i \(-0.224245\pi\)
−0.505492 + 0.862831i \(0.668689\pi\)
\(692\) −14.3790 24.9052i −0.546609 0.946755i
\(693\) 0 0
\(694\) −8.77388 + 15.1968i −0.333052 + 0.576863i
\(695\) 12.3586 4.49818i 0.468790 0.170626i
\(696\) 0 0
\(697\) −1.77151 + 1.48647i −0.0671006 + 0.0563041i
\(698\) 33.9018 28.4470i 1.28320 1.07673i
\(699\) 0 0
\(700\) −21.3485 + 29.3873i −0.806899 + 1.11074i
\(701\) −1.01529 −0.0383469 −0.0191734 0.999816i \(-0.506103\pi\)
−0.0191734 + 0.999816i \(0.506103\pi\)
\(702\) 0 0
\(703\) −2.50807 + 4.34411i −0.0945937 + 0.163841i
\(704\) 0.0369987 0.0134664i 0.00139444 0.000507534i
\(705\) 0 0
\(706\) −3.03381 17.2056i −0.114179 0.647540i
\(707\) −20.8814 + 5.20761i −0.785327 + 0.195852i
\(708\) 0 0
\(709\) −42.0314 + 15.2982i −1.57852 + 0.574535i −0.974882 0.222723i \(-0.928505\pi\)
−0.603639 + 0.797258i \(0.706283\pi\)
\(710\) −51.7319 89.6023i −1.94146 3.36271i
\(711\) 0 0
\(712\) 0.708440 1.22705i 0.0265499 0.0459858i
\(713\) 24.3192 8.85147i 0.910762 0.331490i
\(714\) 0 0
\(715\) 1.11287 0.933808i 0.0416189 0.0349224i
\(716\) 20.4188 + 7.43184i 0.763087 + 0.277741i
\(717\) 0 0
\(718\) −5.06175 + 28.7066i −0.188903 + 1.07132i
\(719\) 2.63441 4.56292i 0.0982467 0.170168i −0.812712 0.582665i \(-0.802010\pi\)
0.910959 + 0.412497i \(0.135343\pi\)
\(720\) 0 0
\(721\) 15.2333 + 7.42867i 0.567316 + 0.276658i
\(722\) −6.98286 + 39.6017i −0.259875 + 1.47382i
\(723\) 0 0
\(724\) −2.40419 + 2.01735i −0.0893510 + 0.0749744i
\(725\) 1.52874 + 0.556414i 0.0567758 + 0.0206647i
\(726\) 0 0
\(727\) 31.0047 + 26.0161i 1.14990 + 0.964882i 0.999717 0.0237758i \(-0.00756878\pi\)
0.150185 + 0.988658i \(0.452013\pi\)
\(728\) −0.526155 0.256585i −0.0195006 0.00950969i
\(729\) 0 0
\(730\) 46.7579 + 80.9870i 1.73059 + 2.99746i
\(731\) 3.97838 1.44801i 0.147146 0.0535567i
\(732\) 0 0
\(733\) −18.8382 + 15.8071i −0.695804 + 0.583849i −0.920577 0.390562i \(-0.872281\pi\)
0.224772 + 0.974411i \(0.427836\pi\)
\(734\) −52.5972 19.1438i −1.94140 0.706610i
\(735\) 0 0
\(736\) 5.49004 31.1356i 0.202366 1.14767i
\(737\) 37.9040 1.39621
\(738\) 0 0
\(739\) 41.2905 1.51890 0.759448 0.650568i \(-0.225469\pi\)
0.759448 + 0.650568i \(0.225469\pi\)
\(740\) 2.75215 + 2.30933i 0.101171 + 0.0848927i
\(741\) 0 0
\(742\) 16.8448 4.20093i 0.618393 0.154221i
\(743\) 8.19507 6.87648i 0.300648 0.252274i −0.479966 0.877287i \(-0.659351\pi\)
0.780614 + 0.625013i \(0.214907\pi\)
\(744\) 0 0
\(745\) 9.11896 51.7162i 0.334093 1.89474i
\(746\) 42.2663 1.54748
\(747\) 0 0
\(748\) 0.964765 1.67102i 0.0352753 0.0610986i
\(749\) −31.3978 3.29821i −1.14725 0.120514i
\(750\) 0 0
\(751\) 2.25015 + 12.7612i 0.0821092 + 0.465664i 0.997943 + 0.0641070i \(0.0204199\pi\)
−0.915834 + 0.401557i \(0.868469\pi\)
\(752\) 27.8970 + 10.1537i 1.01730 + 0.370266i
\(753\) 0 0
\(754\) 0.00569717 0.0323103i 0.000207479 0.00117667i
\(755\) 67.5716 2.45918
\(756\) 0 0
\(757\) 28.7036 1.04325 0.521625 0.853175i \(-0.325326\pi\)
0.521625 + 0.853175i \(0.325326\pi\)
\(758\) −5.68081 + 32.2175i −0.206336 + 1.17019i
\(759\) 0 0
\(760\) −39.6537 14.4328i −1.43839 0.523532i
\(761\) 6.50686 + 36.9023i 0.235874 + 1.33771i 0.840766 + 0.541399i \(0.182105\pi\)
−0.604892 + 0.796307i \(0.706784\pi\)
\(762\) 0 0
\(763\) −0.344905 0.774548i −0.0124864 0.0280405i
\(764\) −4.53352 + 7.85229i −0.164017 + 0.284086i
\(765\) 0 0
\(766\) −39.9321 −1.44280
\(767\) 0.0889913 0.504695i 0.00321329 0.0182235i
\(768\) 0 0
\(769\) −25.1958 + 21.1418i −0.908584 + 0.762392i −0.971849 0.235605i \(-0.924293\pi\)
0.0632654 + 0.997997i \(0.479849\pi\)
\(770\) −33.3594 34.5407i −1.20219 1.24476i
\(771\) 0 0
\(772\) 2.52531 + 2.11899i 0.0908879 + 0.0762640i
\(773\) 18.3980 0.661731 0.330866 0.943678i \(-0.392659\pi\)
0.330866 + 0.943678i \(0.392659\pi\)
\(774\) 0 0
\(775\) −57.2583 −2.05678
\(776\) 0.501203 2.84246i 0.0179921 0.102038i
\(777\) 0 0
\(778\) −15.2639 5.55560i −0.547237 0.199178i
\(779\) 16.2988 13.6763i 0.583966 0.490006i
\(780\) 0 0
\(781\) 32.6856 11.8966i 1.16958 0.425693i
\(782\) −3.45950 5.99202i −0.123711 0.214274i
\(783\) 0 0